#### Question

# What is the formula of the hydrate?

A 15.67g sample of a hydrate of magnesium carbonate was carefully heated, without decomposing the carbonate, to drive off the water. The mass was reduced to 7.56 g. What is the formula of the hydrate?

Please explain.

#### Answer

The mass of water lost = initial masss - final mass = 15.67 g - 7.56 g = 8.11 g. The molar mass of H2O = 18.0 g/mole.

8.11 g H2O x (1 mole H2O / 18.0 g H2O) = 0.451 moles H2O

The amount of MgCO3 left = 7.56 g. The molar mass of MgCO3 = 84.3 g/mole.

7.56 g MgCO3 x (1 mole MgCO3 / 84.3 g MgCO3) = 00897 moles MgCO3.

So the ratio of moles H2O / moles MgCO3 = 0.451 / 0.0897 = 5.03

That means that there are 5 moles of H2O fopr every 1 mole of MgCO3. The formula of the hydrate is MgCO3 x 5H2O.

you have 15.67g of a hydrated MgCO3. 7.56 g of that is solid MgCO3, the rest is water or 8.11g.

8.11gH2O / 18g/mole = 0.45 moles H2O

7.56g MgCO3 / 84.3g/mole = 0.09 moles MgCO3

divide by the smallest number to get the molar ratio

0.45 / 0..09 = 5 for H2O

0.09 / 0.09 = 1 for MgCO3

MgCO3-5H2O

A 15.67g sample of a hydrate of magnesium carbonate was carefully heated, without decomposing the carbonate, to drive off the water. The mass was reduced to 7.56 g. What is the formula of the hydrate?

Equation for dehydrating a hydrate of magnesium carbonate is shown below:

MgCO3 ? x H2O → MgCO3 + x H2O

The equation above states that 1 mole of MgCO3 ? x H2O will produce 1 mole of MgCO3 + 1 mole of x H2O.

1 mole of MgCO3 has a mass of 24.3 + 12 + (3 * 16) = 84.3 grams

7.56 grams of MgCO3 = 7.56 ÷ 84.3 = 0.0897 moles of MgCO3

1 mole of H2O has a mass of 18 grams

x moles of H2O has a mass of (x * 18) grams

1 mole of MgCO3 ? x H2O has a mass of 84.3 + (x * 18) grams

15.67 grams of MgCO3 ? x H2O = 15.67 ÷ [84.3 + (x * 18)] moles of MgCO3 ? x H2O.

1 mole of MgCO3 ? x H2O will produce 1 mole of MgCO3, so

[84.3 + (x * 18)] moles of MgCO3 ? x H2O will produce 0.0897 moles of MgCO3.

15.67 ÷ [84.3 + (x * 18)] = 0.0897

Multiply both sides by [84.3 + (x * 18)]

15.67 = 0.0897 * [84.3 + (x * 18)]

15.67 = (0.0897 * 84.3) + (0.0897 * 18) * x

Subtract (0.0897 * 84.3) from both sides

15.67 – (0.0897 * 84.3) = (0.0897 * 18) * x

x = [15.67 – (0.0897 * 84.3)] ÷ (0.0897 * 18)

x = 5.02

The formula of the hydrate is MgCO3 ? 5 H2O